Catadioptrical lens



p 1940- R'. E. BITNER CATADIOPTRICAL LENS Filed Oct. '28, 1959 2Shoets-Sheet 2 fl? CE L'- -3.es

x EN N///// mij? m INVENTOR Patented Spt. 24, 1940 UNITED sTArEs P'ATENT OFFICE u CATADIOPTRICAL LENS Ralph n. Bitner, New york', N. Y;Application October 28, 1939, Serial No; ,301315 I p 6Claims. Thisinvention relates to lens units that both reflect and refract and moreparticularly relates to I lenses cast from a singleblock of transparentmaterial, the surfaces of which are aspherical.

x The use of asphe'rical surfaces tor-lens units wasflrst proposed manyyears ago by some of the first investigators incptical science.- It hasbeen shown that these surfaces, called 'fcartesian" sur tured because ofthe difllculties in grinding and" polishing. Recently, howeve', with theadvent'of mouldable synthetic' resins of good optical quali-` ties, itis possible toproduce at a reduced cost,

aspherical lenses of high qualit such a lens is described in the U.-'S.Patent No. 2,086,286, issued flgiration in this case is not specified.

U. S. Patent No. 1,507,212 issued to L. Silberstein, illustrates theapplication of an aspherical surface to part of a lens system and givesmathematical equations for calculating such surfaces.

The present 'invention employs a single block of transparent materialwith a'cavi'ty at one side thereof, symmetrical. about the opticalaxis,`in

which the source of light is positioned. v The walls of this cavity areformed with s'urface's of revolution which refract 'the rays of light'from the 4 source and; direct .them through the lens in three welldefin'edpencils., One of'these, the central 'or 40 paraxial pencil, isagain refracted by an exit sur-' face and is threby 'renderedparalleiThe o'ther' pencils are firstinternally refiected and then re- V iractedat the exit surface into two other` par-` allel beams, all threeresultant bean's being parallel to the opticalaxis'. All surfaces used'are surifaces. of revolution' taken around the optical axi's 'nd all'are khowngener'ally 'as "Cartesian' a I The'lens block'is so' designed'as 'to be moulded in a-simpletwopiece mouldof anysuit able transparentmaterial but preferably of transsura'ces.

to N. M. Stanley, although the exact surface conparent' synthetic resin;-since the source is sur-` roundedby the lens it` is possible to utilizeall luminous fiux radiated,.an d project it all in a single parallelbeam. By designing the reflect-` ing surfaces of the lens -unit toreceive the in-- 5 cident beams at' a greater angle than the criticalangle total reflection 'is obtained without the use of silvering-or anyother metallic reflector.

Throughout this specificationtherelative position of `'lines andsurfaces will ,be indicated by 10 speclfying the angl between the lineand a nora mal to the surface. v

One'of the objects of the invention is to pro- -vide a lens unit castfrom a single block of transparent material which willfocus practicallyall 15 the available light rays into, a single parallel beam.Anotherobject of the invention is to provide a singe lens unit whichreflects the marginal and intermediate rays by means of total internalreflection, thereby eliminating the necessity of me- 20 tallicreflectors. i

Another object of the invention is to provide a lens of easily mouldablematerial having refractingand reflecting surfaces free from sphericalaberration. v I

Another object of the invention is to provide a v flashlight -lens unitwhich will gather in and focus' all the. available light rays from acommercial flashlight lamp. a 4

Another object of 'the invention is to provide an 3 eflicient lenswhichhas 'a small overall diameter in comparison to the size of the source,generallyhaving a ratio of less than three. Still another object of theinvention-is to provide a lens whichmay be'moulded of synthetic 35 resinor -other suitable: material in a' simple two piece mouldby automaticnachinery. p Other objects and struct al details of the invention willbe apparent from the following de-' scription when read in connectionwith 'the ac- 40 companying drawings, 'Wherei'n I Fig. 1. is a sectionalviewtaken ona meridian plane of, the lens unit, showing the associated 4curves u's'ed'in forming the surfacesg f c `Fig.:2: is a half sectionalView showing-that 5` part of the lens blocktnearest the-source. l i

Fig. 3 is' aisectional view of the reiracting entrance ;surface,,adjoining .thatjshown in '21 with 'dinension's showing its fo'callength and axial' j inclination." "5 0 Fig. 4 is a sectional view ofanother refracting entrance surface adjoining that shown in Fig. 3 andsimilar to it except for focal length and axial displacement.

Fig. 5 is a sectional view of one of the reflecting surfaces showing thecharacteristics of the parabola from which it is taken. Fig. 6 isasectional view of the second reflecting surface, similar to Fig. 5except for axial displacement and focal length.

Fig. 7 is a sectional View of the two exit surfaces, both shown as apart of the ellipsoid from which they were derived.

Referring now to Fig. 1, the lens block 20 is indicated with an opticala'xis 2l-2l and a source of light f onsaid axis. This source may be anyconvenient lamp or light image but the present design is intended to'beused 'with a small flashli'ght bulb. The lens unit is a solid 'blockbounded by eight faces, all surfaces of revolution about the opticalaxis 2l-2l. These surfaces are as follows: (1) A paraxial .entrancesurface A consisting of an aspherical quart'ic surface of revolu- 'tionwhich receives the light rays from the source f and refracts them to avirtual focus of fz. (2) A refracting entrance surface B consisting of aconvex hyperboloid formed by the revolution of a section of a hyperbolaabout the 'axis and refracting therays from f into a beam of parallelrays. (3) A refracting entrance surface C similar to B, except for focallength and axial .optical surfaces but has no optical function of itsown. (6) a reflecting surface F similar to D but receiving parallel raysfrom surfaceB and reflecting them by a different path toward the pointfa. (7) A refracting concave exit surface G consisting of an ellipsoidformed by the revolution of a section of an eliipse about the opticalaxis and refracting. the light rays received from surfaces D and F'intoa beam of parallel rays. (8) A refracting paraxlal exit surface H formedby the revolution of a section of an ellipse about the optical axis andrefracting the light rays coming in the direction from the virtualfocus' u j2 into a beam of parallel rays.

Each of these eight' surfaces will now be considered in detail andmethods and means for their computation disclosed. Fig. 2 is designed toshow some of the more important characteristics of paraxial surface A.The optical axis is represented by the line 2I-2l as in Fig. 1.' Thesource f is placed .275 unit-from the axial surface point 22 and thevirtual focal point ;fz from which the refracted rays appear tooriginate, is just twice this distance or .55 unit. The resultantcurvature of face A is far from a spherical surface and may change itscurvature from convex i at the axis to concave near the rim. Theequation of this curve, as generally expressed in terms of thecoordinates of any point 'on the curve, is a complicated fourth degreeequation or quartic and is very difficult to compute. Silber- .stein inPatent 1,507,212 gives an approximate method 'of solution by expansioninto a series. I prefer, however, to calculate such curves by using aparametric form 'with the length of optical path as the parameter. Inaccordance with the fundamental concepts of image formation, thisequation is G' -a+ub where a is the length of .the incident ray, b thelength of the refracted ray, the refractive index and G a constantquantity. When a virtual image is formed, as is the case in Fig. 2, thelength b is considered negative, hence the equation becomes G=,a-;.b.From the geometrical construction as shown in Fig. 2 it is obvious thatthe following relations are true:

a =b +c -2bc cos a. X=b cos a.

By suitable rearrangement we get:

where X and Y are the coordinates of any point on the required curve andthe parametric quant y This series of equations may be used forcomputing the points on the refracting surface and a 'much simpler andshorter method results. It has one disadvantage overthe older method in'that neither the value of' X or Y- is known at the start of thecomputation. This feature is of no consequence, however, when a curve isto be computed with a large number of points.

The lens block herein'disclosed was designed for a lens material havingan index of refraction equal to 1.52. It is obvious that other similarlenses may be designed within the scope of this invention which havedifferent indices of refraction.

Fig. 3 shows the construction of a convex refracting surface B whichadjoins' the surface shown in Fig. 2. This part of the lens receiveslight rays emanating from the source !i on the optical axis and refractsthem into a parallel beam. The curve is a hyperbola with its apex .3unit from the 'source and an eccentricity of 1.52. The portion used inthe lens block is designated by the line 23-24 and the angular tilt of56 given theaxis is to assure easy withdrawal of the die during themoulding operation.

Fig. 4 shows the construction of the hyperboloid similar to the one inFig. 3 except for focal length and axial tilt. As may be seen from Fig.1,

this refracting surface C adjoins the surface B. Its axis is 78" fromthe optical axis of the lens block with the apex being .35 unit from thesource of light f. The line between the points 24-25 denotes the segmentused in the block. The eccentricity of this curve is also 1.52.

Figs. 5 and' 6 show'the characteristics of a pair of parabolas which areused to form surfaces of revolution about the main optical axis. The useof paraboloids as focussing means is quite old in the flashlight artbut' prev 'as structures have placed the light source at ne focus of theparaboloid to obtain a reflected parallel bea'm directly. The presentdesign uses the paraboloid in a reversed manner since the parallel lightrays are received by the mirror and reflected toward the focal point fa.The dire tion of light with respect to the paraboloid is, therefore,opposite to that in general usage.

The primary reason for employing the paraboloids in this manner is 'tosav'e space. If the older design were employed, the resultant diameterof the lens block would be greatly increased. Another advantage of usingparaboloids for point concentrated as it leaves the lens and thereforepermits the formation of a smaller and more intense spot of light.

It will be'obvious from the drawings (Figs. 1, 3,

and 6 that the hyperboloid B and the parab oloid Fcoop'erate'to directthe same pencils of light from the source f to a point !a on'the axis.These points are spaced &units apart. The hyperboloid B is formed withits axis 56 from the optical axis, hence the axis of theparaboloid F issimilarly disposed. The dimensions as indicat'ed in Figs. 3, 4, 5, and 6are in units of any system 'of measurement, the radiusof the circleforming the exit edge of-the block being taken as one.

The refracting hy'perboloid C and the reflecting paraboloid D, as shownin Figs. 1, 4, and 5, also cooperate to direct another group of lightrays from the source 'J' toward'the point fa. Both of these sectionshave the same axial inclination,

. 78. this value being a result of an efl'ort to keep the reflectingangle in the paraboloid well within the limit for total internal*reflection and at the same time gatherin as much light from the sourceaspossible. The limiting angle for total reflection in a medium with arefractive index of 1.52'is 41 8' 20".

Fig; 7 illustrates the formation of exit surfaces G and H, bothellipsoids and both refracting.

Every refracting ellipsoid must have its eccen trlcity equal to thereciprocal of the refractive index of the medium, hence one figure maybe used for both surfaces although in the actual lens block, surface Gis derived from an ellipse 3.5 times as large as the ellipse used toform the surface H.

The 'extent of surface G is indicated by angular boundaries, 11 40' and5, wth point fa taken as a center. The distance L is 3.5 units. As mayflected from surfaces D and F, directed toward the point fa. The concaveellipsoid G renders these rays parallel to the optical axis. The ellipsewhich forms this surfacehas a major axis (28-21) of 4.222 units and aminor axis of 3.18 units. The distance between foci is 2.7777 units.surface H is a convex ellipsoid which refracts the rays of light thathave been refracted by surface A. While in the lens block, these rays'are divergent with fz as a virtualfocus. The

surface H renders them parallel to .the optical axis. The focal distanceK of this lens component, measured from fz' to the axia boundary 21, is1 unit and therefore all characteristic values of the generating ellipsewill have to be reduced in the ratio 3.5 to 1 as Compared to the valuesgiven in the above paragraph.

While I have described what I consider to be a highly desirableembodiment of my invention,

it is obvious that many changes in form could be made without departingfrom the spirit of my invention, and Itherefore, do not limit 'myself tothe exact form herein shown and described nor F to anything less thanthe whole of my invention` as hereinbefore 'set forth, and hereinafterclaimed.

I claim:

1. A lens bloc for-focussing light from a concentrated source into apairallei beam having in combination; one paraxial lens component andtwo marginal lens mirror combinations; said paraxal lens comprising aquartic entrance surface and a convex ellipsold exit surface, both ofsaid 'surfaces having their axes coincident with the optical axis of thelens block; one of said &215300 nirrr -combinations composed of marginallens a hyperboloid refracting entrance surface, a pa-` of saidhyperboloid and said paraboloid disposed at equal angular inclinationsto the optical axis of the block; the second of said marginal lensmirror combinations composed of a hyperboloid refracting entrancesurface, a paraboloid tota-l internalreflection mirror and a concaveellipsoid refracting edt surface, the axes of said hyperboloid and saidparaboloid disposed at equal angular inclinations to the optical axis oftheblock: the flrst mentioned hyperboloid having a focal length which issubstantially less than the focal length of the second mentionedhyperboloid; said second concave ellipsoid exit surface being acontinuation of the first mentioned concave ellipsoid exit surface andall of said surface components being surfaces of revolution about theoptical axis.

2. A lens block for focussing light from a concombinatiomone paraxiallens component and ,two *margihal lens mirror combinations; saidparaxial lens comprising a quartic entrance surface and a convex.ellipsoid said surfaces having their axes coincident with the opticalaxis of the lens block; one of said marginal lens mirror combinationscomposed of a hyper-boloid refraction entrance surface, aparaboloidtotal internal reflection mirror, and a concave ellipsoid refractingexit surface, the axes of said hyperboloid andsaid parabololddisposed'at equal angular inclinations to 'the optical axis of theblock; the second of said marginal lens mirror combinations composed 'ofa hyperbooid refracting ntrance surface, a paraboloid total internalreflection mirror and a concave ellipsoid refracting exit surface. theaxes of said hyperbooid and said paraboloid disposed at equal an-'"axis.

3. A lens block for focussing light from a concentrated source into abarallel beam having in combination; one paraxial lens `component andtwo marginal lens mirror combinations; said paraxial lens comprising aquartic entrance surface and a convex ellipsoid exit surface., both ofsaid surfaces having their axes coincident with theoptical axis of thelensblock; onevof said marginal lens mirror combinations .composed of ahyperboloid refracting entrance surface, a paraboloid total internalreflection mirror, and a concave ellipsoid refracting exit surface, theaxes of said' hyperboloid and said paraboloid disposed at equal angularinclinations to the optical axis of the block; the second of saidmarginal lens ,mirror combinations composed of a hyperboloid refractingentrance surface, a paraboloid total internal reflection-mirror, and aconcave ellipsoid refracting exit surface, the axes of said hyperboloidand said paraboloid disposed at equal angular inclinations to theoptical axis of the block;

' about the optical axis.

4. A lens block for focussing light from a conexit surface, both of aplurality of marginal lens mirror combina'tions; said paraxial lenscomprising a quartic entrance .V surface and a convex .ellipsoid exitsurface, both of said surfaces having their axe's coincident with theoptical axis of the lens block; said plurality of lens mirrorcombinations each. composed of a hyperboloid refracting entrancesurface, a paraboloid total internal reflection mirror and a concaveellipsoid refracting exit surface, the axs of said hyperboloid and saidparaboloid in any one of said combinations disposed at equal angularinclinations to the axis of the block; and all of said surfaceComponents being surfaces of revolution about the optical axis.

5. A lens block for focussing light from a con? centrated source into aparallel beam having ,in

combination; one paraxial lens component and' a plurality of marginallens mirror combinations; said paraxial lens comprising a quarticentrance surface and a convex ellipsoid exit surface, both of saidsurfaces having their axes coincident with the optical axis of the lensblock; said plurality of lens mirror combinations eachcomposed of ahyperboloid refracting entrance surface, a paraboloid total internalreflection mirror and a concave ellipsoid refracting exit surface, theaxes of said hyperboloid and said paraboloid in anyone of saidcombinations disposed at equal anguiar inclinations to the optical axisof the block; the axial angular inclinations of said combinations beingsubstantially difierent, one from the other and all of said surfacecomponents being surfaces of revolution about the optical axis.

6. A lens block for focussing light from a concentrated source into aparallel beam having in combination; one paraxia lens component and aplurality of marginal lens mirror combinations; said paraxial lenscomprising a quartic entrance and a convex ellipsoid exit surface; bothof said surfaces having their axes coincident with the opticai axis ofthe lens block; said plurality of lens mirror combinations each composedof a

